Interface Lattice<E>

All Superinterfaces:
Set<E>
All Known Implementing Classes:
Boolean
public interface Lattice<E> extends Set<E>
A lattice is a set equipped with two commutative, associative and idempotent binary operations: join (∨) and meet (∧), connected by absorption laws.

Mathematical Definition

A lattice (L, ∨, ∧) satisfies:

  • (L, ∨) is a semilattice (Join)
  • (L, ∧) is a semilattice (Meet)
  • Absorption Laws:
    • a ∨ (a ∧ b) = a
    • a ∧ (a ∨ b) = a

Examples

  • Boolean Algebra ({0,1}, OR, AND)
  • Power Set (P(S), ∪, ∩)
  • Natural Numbers (â„•, max, min)
  • Divisibility (â„•, lcm, gcd)
Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Method Summary

    Modifier and Type
    Method
    Description
    E
    join(E a, E b)
    The join operation (∨, least upper bound).
    E
    meet(E a, E b)
    The meet operation (∧, greatest lower bound).

    Methods inherited from interface Set

    contains, description, isEmpty

  • Method Details

    • join

      E join(E a, E b)
      The join operation (∨, least upper bound).
      Parameters:
      a - first operand
      b - second operand
      Returns:
      a ∨ b

    • meet

      E meet(E a, E b)
      The meet operation (∧, greatest lower bound).
      Parameters:
      a - first operand
      b - second operand
      Returns:
      a ∧ b